English

Anabelian geometry with etale homotopy types

Number Theory 2016-12-12 v2 Algebraic Geometry Algebraic Topology

Abstract

Anabelian geometry with etale homotopy types generalizes in a natural way classical anabelian geometry with etale fundamental groups. We show that, both in the classical and the generalized sense, any point of a smooth variety over a field k which is finitely generated over Q has a fundamental system of (affine) anabelian Zariski-neighbourhoods. This was predicted by Grothendieck in his letter to Faltings.

Keywords

Cite

@article{arxiv.1504.01068,
  title  = {Anabelian geometry with etale homotopy types},
  author = {Alexander Schmidt and Jakob Stix},
  journal= {arXiv preprint arXiv:1504.01068},
  year   = {2016}
}

Comments

33 pages, refereed version

R2 v1 2026-06-22T09:10:10.336Z